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```Appendix II                             887

heat-weight^ Rankine the thermodynamic function, and Clausius the
entropy ; the last term being now universally applied.

We may now draw a diagram of heat changes by plotting r to
a base of 0 as in Fig. 844, from which we may deduce

Heat supplied or rejected  =  \$ x mean r.

Just as the fv curve shews work done, and is a cycle of
mechanical operations, so the T<J> curve shews heat change, and is
a cycle of thermal operations. It was first practically developed
by Mr. J. McFarlane Gray, and its great value is apparent when
one remembers how much heat is unrepresented on the j>v
diagram; though both diagrams have their uses. Isothermals,
having constant temperature, are horizontal straight lines on the
ry diagram ; and adiabatics are vertical straight lines, for no heat
is being supplied and yet T changes, <j> (r1-r2) = o and 0 = o, or
entropy is unaltered (see Fig. 844).

Applying to the Carnot cycle, Fig. 844, heat supplied is the
area H1? and that rejected the area H2, for A B, c D are isothermals,
and B c, D A adiabatics. Also the work done is Ht - H2

-T, «. .                 work done          H, - BL      r, - r<>

.-. Efficiency =  , — —   — — -    =    .* -  • 2 =   l     2
heat expended           Hx           Ti

To draw the r 0 diagram for water and steam, shewing heat
supplied per Ib. weight, we commence with an arbitrary zero of
entropy at 32° Fahr. =492° absolute. Then                             !

Entropy of water at 492° = o
and at any otheil temperature r
#w  = loger~

from which Table I. (n,ext page) is calculated, and the results
plotted as curve AB, Fig. 845, the area under which shews heat
supplied up to any temperature.

* Hyperbolic log. = comm on log. x 2 3026.```